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Bornological Convergences on the Hyperspace of a Uniformizable Space

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Abstract

Bornological convergence is a generalization of the well known Attouch–Wets convergence. Our aim is to compare lower, upper and “two-sided” convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.

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Correspondence to Marco Rosa.

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Rosa, M., Vitolo, P. Bornological Convergences on the Hyperspace of a Uniformizable Space. Set-Valued Var. Anal 24, 597–618 (2016). https://doi.org/10.1007/s11228-015-0359-y

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Keywords

  • Hyperspace
  • Attouch–Wets topology
  • Bornological convergence
  • Uniform space
  • Bounded-proximal topology

Mathematics Subject Classification (2010)

  • Primary 54B20
  • Secondary 54E15
  • 54A20